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Q.11

Expert-verified

The Practice of Statistics for AP

Found in: Page 525

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favour the proposal. Of these, 89 say “Yes.”
(a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions.
(b) Based on your work in part (a), can the U.S. Forest Service conclude that more than half of visitors to Yellow-stone National Park favour the proposal? Justify your answer.

a. the confidence interval is $(0.49, 0.70)$

b. No

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

step 1: introduction

Given, the service asks a random sample n = $150$

people who say yes x = $89$

Using,

$\hat{p} - z_{\frac{a}{2}} \times \sqrt{\frac{\hat{p} \times (1 - \hat{p})}{n}} < p < \hat{p} - z_{\frac{a}{2}} \times \sqrt{\frac{\hat{p} \times (1 - \hat{p})}{n}}$

$99 %$ confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions is $(0.49, 0.70)$

step 2: explanation

From the above part, it is realized that the population extent is somewhere in the range of $0.49$ and $0.70$ . No, the U.S. Forest Service cant conclude that more than half of visitors to Yellow-stone National Park favour the proposal since the interval has the range $0.49$ . Accordingly, it can't be inferred that the greater part of the guests are supportive of the proposition.

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Interpret the interval in context. Putting It All Together

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